BACKGROUND

When describing these time series, we have used words such as “trend” and “seasonal” which need to be defined more carefully.

Trend A trend exists when there is a long-term increase or decrease in the data. It does not have to be linear. Sometimes we will refer to a trend as “changing direction”, when it might go from an increasing trend to a decreasing trend, like this figure;
SIC Trend

SIC Trend

Seasonal A seasonal pattern occurs when a time series is affected by seasonal factors such as the time of the year or the day of the week. Seasonality is always of a fixed and known period.

All this analysis are do to SubArea 48.1 in the Southern Ocean.

OBJECTIVE

To condition an operational model in krill, the chosen environmental component must have an associated error (variance) to be incorporated, which gives more reliability to the projection of the population variables.

library(here)
library(tidyverse)
library(tsibble)
library(zoo)
library(feasts)
library(kableExtra)

Read data. This data is from another analysis with raster layer from satellite sources.

load("DataEnvKrill2.RData")
# ls()
#cargo objeto
dtats <- get("dataenvf2")

Time Series SIC

Data wrangling to clean it, becauso have different structure and NA, wich is not supported.

dtats1 <- dtats %>% 
  select(1,2,4,6) %>% 
  mutate(ANOn =as.numeric(ANO)) %>% 
  drop_na(ANOn)

Change dtats1 from data.frameto ts object.

ts_obj <- ts(dtats1$meansic, 
             start = c(dtats1$ANOn[1], 1), 
             end = c(dtats1$ANOn[length(dtats1$ANOn)], 12), 
             frequency = 12)

ts_tbobj <- as_tsibble(ts_obj)

A subseries plot to show difference.

ts_tbobj |>
  gg_subseries(value) +
  labs(
    y = "SIC",
    title = "SIC SubArea 48.1"
  )+
  theme_bw()

### Autocorrelacion

An scaterplot of correlation simple bettwen lags. We select 60 lags, to get entire series of SIC.

ts_tbobj %>% 
  gg_lag(value, 
         geom="point",
         lags = 1:12)

ts_tbobj |> 
  ACF(value, lag_max = 60) %>% 
  autoplot() +
  labs(title = "Autocorrelacion de SIC in 48.1")+
  theme_bw()

We then describe a trend correlation and also a seasonal one, which is very characteristic of environmental data.

Descomposicion

In this chapter, we consider the most common methods for extracting these components from a time series. Often this is done to help improve understanding of the time series, but it can also be used to improve forecast accuracy.

When decomposing a time series, it is sometimes helpful to first transform or adjust the series in order to make the decomposition (and later analysis) as simple as possible. So we will begin by discussing transformations and adjustments.

dcmp <- ts_tbobj|>
  model(stl = STL(value))
kableExtra::kable(components(dcmp))
.model index value trend season_year remainder season_adjust
stl 1979 Jan 269.8668 275.0351 2.2167994 -7.3850723 267.6500
stl 1979 Feb 288.8191 270.7114 -4.2521462 22.3598051 293.0712
stl 1979 Mar 279.6058 266.3878 -9.5103727 22.7283467 289.1161
stl 1979 Apr 241.2115 262.0641 -11.4438873 -9.4087415 252.6554
stl 1979 May 245.8812 257.8834 18.5281032 -30.5302798 227.3531
stl 1979 Jun 236.1422 253.7026 -28.6910940 11.1307286 264.8333
stl 1979 Jul 211.0045 249.5218 2.4606864 -40.9779803 208.5438
stl 1979 Aug 229.8812 245.4016 -7.6737636 -7.8466914 237.5550
stl 1979 Sep 300.5779 241.2815 2.4988425 56.7975235 298.0790
stl 1979 Oct 280.1062 237.1613 32.8317624 10.1131077 247.2744
stl 1979 Nov 193.5068 234.9515 -10.4304026 -31.0143719 203.9372
stl 1979 Dec 223.6958 232.7417 13.7313630 -22.7773031 209.9644
stl 1980 Jan 243.1989 230.5319 0.2202396 12.4467861 242.9787
stl 1980 Feb 194.8713 229.0798 -4.1716442 -30.0368483 199.0429
stl 1980 Mar 217.8992 227.6277 -10.3256997 0.5972246 228.2249
stl 1980 Apr 214.3996 226.1756 -10.7432952 -1.0326153 225.1429
stl 1980 May 241.8272 226.9967 20.2261944 -5.3957135 221.6010
stl 1980 Jun 191.7426 227.8179 -27.6448982 -8.4303807 219.3875
stl 1980 Jul 290.0108 228.6390 3.0987901 58.2730065 286.9120
stl 1980 Aug 182.1188 230.2840 -6.3881819 -41.7770180 188.5070
stl 1980 Sep 208.2682 231.9290 1.7583199 -25.4191123 206.5099
stl 1980 Oct 273.2187 233.5740 30.5849999 9.0596954 242.6337
stl 1980 Nov 207.1053 233.3533 -10.2817236 -15.9662182 217.3870
stl 1980 Dec 229.3843 233.1325 13.9129487 -17.6610885 215.4714
stl 1981 Jan 313.1791 232.9117 -1.7633441 82.0307580 314.9425
stl 1981 Feb 236.0774 234.7345 -4.0693176 5.4121936 240.1467
stl 1981 Mar 256.7147 236.5574 -11.1103536 31.2676656 267.8250
stl 1981 Apr 191.4221 238.3802 -10.0042632 -36.9537818 201.4264
stl 1981 May 217.4239 241.8548 21.9704923 -46.4013117 195.4535
stl 1981 Jun 191.0621 245.3293 -26.5485399 -27.7186903 217.6106
stl 1981 Jul 263.6238 248.8039 3.7910124 11.0288390 259.8327
stl 1981 Aug 181.4527 249.8639 -5.0503306 -63.3608373 186.5031
stl 1981 Sep 226.5905 250.9239 1.0682181 -25.4016746 225.5222
stl 1981 Oct 359.7138 251.9839 28.3811712 79.3486824 331.3326
stl 1981 Nov 299.2565 252.6657 -10.0975979 56.6884420 309.3541
stl 1981 Dec 331.0153 253.3474 14.1151429 63.5527134 316.9002
stl 1982 Jan 255.0153 254.0292 -5.1982902 6.1843829 260.2136
stl 1982 Feb 232.0018 253.6381 -4.5772866 -17.0590212 236.5791
stl 1982 Mar 229.3879 253.2470 -12.6815276 -11.1775407 242.0695
stl 1982 Apr 222.4743 252.8559 -8.6960884 -21.6854704 231.1704
stl 1982 May 261.8056 250.0013 25.4083457 -13.6040755 236.3972
stl 1982 Jun 199.0621 247.1467 -24.9717612 -23.1128470 224.0339
stl 1982 Jul 186.8065 244.2921 5.1919848 -62.6776226 181.6145
stl 1982 Aug 269.8668 244.1661 -2.7649638 28.4656190 272.6318
stl 1982 Sep 288.8191 244.0401 -1.2110652 45.9900026 290.0301
stl 1982 Oct 279.6058 243.9142 23.8318754 11.8597277 255.7739
stl 1982 Nov 241.2115 244.6208 -8.5404083 5.1311183 249.7519
stl 1982 Dec 245.8812 245.3275 15.6230238 -15.0693006 230.2582
stl 1983 Jan 236.1422 246.0341 -8.7173918 -1.1745125 244.8596
stl 1983 Feb 211.0045 243.7741 -5.1458155 -27.6237544 216.1503
stl 1983 Mar 229.8812 241.5140 -14.2896658 2.6568318 244.1709
stl 1983 Apr 300.5779 239.2540 -7.4049123 68.7287961 307.9828
stl 1983 May 280.1062 236.9399 28.8491660 14.3171662 251.2570
stl 1983 Jun 193.5068 234.6258 -23.3854661 -17.7335660 216.8922
stl 1983 Jul 223.6958 232.3117 6.6090228 -15.2249405 217.0867
stl 1983 Aug 243.1989 230.7738 -0.4633895 12.8884878 243.6623
stl 1983 Sep 194.8713 229.2360 -3.4739992 -30.8906697 198.3453
stl 1983 Oct 217.8992 227.6981 19.2988380 -29.0977384 198.6004
stl 1983 Nov 214.3996 227.1526 -6.9670512 -5.7858718 221.3667
stl 1983 Dec 241.8272 226.6070 17.1483703 -1.9282232 224.6788
stl 1984 Jan 191.7426 226.0615 -19.3914905 -14.9274435 211.1341
stl 1984 Feb 290.0108 228.1681 -4.1407480 65.9834795 294.1515
stl 1984 Mar 182.1188 230.2746 -12.2895233 -35.8662957 194.4083
stl 1984 Apr 208.2682 232.3812 -3.8657226 -20.2472428 212.1339
stl 1984 May 273.2187 232.9101 33.4335658 6.8751019 239.7852
stl 1984 Jun 207.1053 233.4389 -18.6959362 -7.6376693 225.8012
stl 1984 Jul 229.3843 233.9678 7.1602163 -11.7436558 222.2241
stl 1984 Aug 313.1791 234.4488 2.0234409 76.7068751 311.1557
stl 1984 Sep 236.0774 234.9298 -2.4334832 3.5810650 238.5109
stl 1984 Oct 256.7147 235.4109 4.3772289 16.9265925 252.3374
stl 1984 Nov 191.4221 238.9050 -7.4047152 -40.0781090 198.8269
stl 1984 Dec 217.4239 242.3991 21.0108235 -45.9859638 196.4131
stl 1985 Jan 191.0621 245.8932 -29.8411260 -24.9899669 220.9032
stl 1985 Feb 263.6238 247.6514 -2.9919849 18.9643582 266.6157
stl 1985 Mar 181.4527 249.4096 -10.2264526 -57.7303812 191.6792
stl 1985 Apr 226.5905 251.1678 -0.3588627 -24.2184474 226.9493
stl 1985 May 359.7138 251.9124 37.8903778 69.9109837 321.8234
stl 1985 Jun 299.2565 252.6571 -14.2142104 60.8136854 313.4707
stl 1985 Jul 331.0153 253.4017 7.4233895 70.1902206 323.5919
stl 1985 Aug 255.0153 253.5775 4.1742468 -2.7364874 250.8411
stl 1985 Sep 232.0018 253.7534 -1.7769961 -19.9745965 233.7788
stl 1985 Oct 229.3879 253.9292 -10.9338396 -13.6074652 240.3218
stl 1985 Nov 222.4743 251.7203 -8.2372692 -21.0086983 230.7116
stl 1985 Dec 261.8056 249.5114 24.5298473 -12.2356530 237.2757
stl 1986 Jan 199.0621 247.3025 -27.1505734 -21.0897780 226.2127
stl 1986 Feb 186.8065 245.9020 1.4618967 -60.5574618 185.3446
stl 1986 Mar 269.8668 244.5016 -2.7760454 28.1411982 272.6428
stl 1986 Apr 288.8191 243.1012 -3.5842036 49.3020637 292.4033
stl 1986 May 279.6058 244.1397 29.8657066 5.6003574 249.7401
stl 1986 Jun 241.2115 245.1782 -10.5053988 6.5387486 251.7169
stl 1986 Jul 245.8812 246.2166 11.2485180 -11.5839760 234.6327
stl 1986 Aug 236.1422 244.8599 -8.2132030 -0.5045225 244.3554
stl 1986 Sep 211.0045 243.5032 -3.4694732 -29.0292596 214.4740
stl 1986 Oct 229.8812 242.1465 -14.3216335 2.0562948 244.2028
stl 1986 Nov 300.5779 239.2762 -5.5951864 66.8968297 306.1730
stl 1986 Dec 280.1062 236.4059 30.6041701 13.0961383 249.5020
stl 1987 Jan 193.5068 233.5356 -24.5693270 -15.4595123 218.0761
stl 1987 Feb 223.6958 232.1581 5.7887968 -14.2510995 217.9070
stl 1987 Mar 243.1989 230.7806 4.5297051 7.8886602 238.6692
stl 1987 Apr 194.8713 229.4030 -6.9317557 -27.5999942 201.8030
stl 1987 May 217.8992 228.1226 21.7412700 -31.9646372 196.1579
stl 1987 Jun 214.3996 226.8421 -6.8336048 -5.6088325 221.2332
stl 1987 Jul 241.8272 225.5616 15.0993768 1.1662086 226.7278
stl 1987 Aug 191.7426 227.2916 -20.4916794 -15.0573220 212.2343
stl 1987 Sep 290.0108 229.0216 -4.9697337 65.9589809 294.9805
stl 1987 Oct 182.1188 230.7515 -17.4468297 -31.1858906 199.5656
stl 1987 Nov 208.2682 231.8984 -2.6201247 -21.0100785 210.8884
stl 1987 Dec 273.2187 233.0453 37.0421238 3.1312703 236.1766
stl 1988 Jan 207.1053 234.1922 -19.3063489 -7.7805661 226.4117
stl 1988 Feb 229.3843 233.9377 6.6230603 -11.1764336 222.7613
stl 1988 Mar 313.1791 233.6832 4.3709931 75.1249269 308.8081
stl 1988 Apr 236.0774 233.4287 -4.3366712 6.9853949 240.4141
stl 1988 May 256.7147 236.3522 5.4330693 14.9293554 251.2816
stl 1988 Jun 191.4221 239.2758 -7.5588023 -40.2948650 198.9809
stl 1988 Jul 217.4239 242.1994 19.7449293 -44.5203591 197.6790
stl 1988 Aug 191.0621 244.8388 -25.2669161 -28.5097867 216.3290
stl 1988 Sep 263.6238 247.4782 -1.2421960 17.3877126 264.8660
stl 1988 Oct 181.4527 250.1177 -9.7592577 -58.9056795 191.2120
stl 1988 Nov 226.5905 251.0271 -2.9547617 -21.4819171 229.5452
stl 1988 Dec 359.7138 251.9366 34.9168161 72.8603619 324.7970
stl 1989 Jan 299.2565 252.8460 -14.1814094 60.5918862 313.4379
stl 1989 Feb 331.0153 253.4600 7.3585250 70.1967638 323.6568
stl 1989 Mar 255.0153 254.0740 4.1527220 -3.2113970 250.8626
stl 1989 Apr 232.0018 254.6879 -1.7585764 -20.9275638 233.7604
stl 1989 May 229.3879 253.2607 -10.8495517 -13.0231733 240.2375
stl 1989 Jun 222.4743 251.8334 -8.2307892 -21.1282505 230.7051
stl 1989 Jul 261.8056 250.4061 24.4713233 -13.0718532 237.3343
stl 1989 Aug 199.0621 247.8621 -29.9722669 -18.8277522 229.0344
stl 1989 Sep 186.8065 245.3181 2.5442722 -61.0559317 184.2622
stl 1989 Oct 269.8668 242.7742 -2.0565318 29.1491634 271.9233
stl 1989 Nov 288.8191 243.6145 -3.3180216 48.5225989 292.1371
stl 1989 Dec 279.6058 244.4549 32.7031635 2.4477430 246.9026
stl 1990 Jan 241.2115 245.2952 -10.6042399 6.5205574 251.8158
stl 1990 Feb 245.8812 245.0404 11.1179175 -10.2771075 234.7633
stl 1990 Mar 236.1422 244.7856 -8.3356902 -0.3076483 244.4779
stl 1990 Apr 211.0045 244.5307 -3.5682446 -29.9579822 214.5727
stl 1990 May 229.8812 241.6452 -14.2855687 2.5215127 244.1668
stl 1990 Jun 300.5779 238.7598 -5.5782870 67.3963839 306.1561
stl 1990 Jul 280.1062 235.8743 30.5960136 13.6359193 249.5102
stl 1990 Aug 193.5068 234.2520 -24.1873839 -16.5578408 217.6941
stl 1990 Sep 223.6958 232.6297 4.2042344 -13.1381378 219.4915
stl 1990 Oct 243.1989 231.0074 2.8398513 9.3516980 240.3591
stl 1990 Nov 194.8713 229.4814 -3.9232640 -30.6868649 198.7946
stl 1990 Dec 217.8992 227.9555 19.1650822 -29.2213537 198.7341
stl 1991 Jan 214.3996 226.4295 -6.7499364 -5.2799304 221.1496
stl 1991 Feb 241.8272 227.0657 15.1823942 -0.4209438 226.6448
stl 1991 Mar 191.7426 227.7020 -20.4910677 -15.4683159 212.2336
stl 1991 Apr 290.0108 228.3382 -5.0771696 66.7497872 295.0880
stl 1991 May 182.1188 230.0901 -17.4531339 -30.5181102 199.5719
stl 1991 Jun 208.2682 231.8419 -2.7343615 -20.8393401 211.0026
stl 1991 Jul 273.2187 233.5938 36.8350989 2.7898221 236.3836
stl 1991 Aug 207.1053 233.4332 -18.3853919 -7.9425022 225.4907
stl 1991 Sep 229.3843 233.2726 5.7840200 -9.6722899 223.6003
stl 1991 Oct 313.1791 233.1120 7.5718615 72.4952444 305.6073
stl 1991 Nov 236.0774 234.7641 -4.7770755 6.0903749 240.8545
stl 1991 Dec 256.7147 236.4162 5.3373734 14.9610934 251.3773
stl 1992 Jan 191.4221 238.0683 -7.7585845 -38.8875742 199.1807
stl 1992 Feb 217.4239 241.5313 19.6390007 -43.7463217 197.7849
stl 1992 Mar 191.0621 244.9942 -25.3797327 -28.5523869 216.4418
stl 1992 Apr 263.6238 248.4572 -1.3606076 16.5271817 264.9844
stl 1992 May 181.4527 249.6885 -9.8108372 -58.4249468 191.2636
stl 1992 Jun 226.5905 250.9199 -2.9660605 -21.3633507 229.5565
stl 1992 Jul 359.7138 252.1512 34.9383805 72.6241796 324.7754
stl 1992 Aug 299.2565 252.9138 -14.5531350 60.8958654 313.8097
stl 1992 Sep 331.0153 253.6764 8.8583793 68.4805428 322.1569
stl 1992 Oct 255.0153 254.4390 0.4417901 0.1345481 254.5735
stl 1992 Nov 232.0018 253.8804 -3.9272045 -17.9513825 235.9290
stl 1992 Dec 229.3879 253.3218 -6.4432221 -17.4906499 235.8312
stl 1993 Jan 222.4743 252.7632 -8.2540099 -22.0348772 230.7284
stl 1993 Feb 261.8056 249.8844 24.5354461 -12.6142784 237.2701
stl 1993 Mar 199.0621 247.0056 -29.9019425 -18.0415423 228.9640
stl 1993 Apr 186.8065 244.1268 2.6088657 -59.9291543 184.1976
stl 1993 May 269.8668 244.1048 -2.0291731 27.7911363 271.8960
stl 1993 Jun 288.8191 244.0829 -3.1775802 47.9137844 291.9967
stl 1993 Jul 279.6058 244.0609 32.9426535 2.6021752 246.6631
stl 1993 Aug 241.2115 244.7110 -10.9069915 7.4075154 252.1185
stl 1993 Sep 245.8812 245.3611 11.6595208 -11.1393953 234.2217
stl 1993 Oct 236.1422 246.0111 -7.0008946 -2.8680192 243.1431
stl 1993 Nov 211.0045 243.7378 -3.4293419 -29.3039545 214.4338
stl 1993 Dec 229.8812 241.4645 -18.5718818 6.9886044 248.4531
stl 1994 Jan 300.5779 239.1911 -5.4418056 66.8285292 306.0197
stl 1994 Feb 280.1062 236.9585 30.7962393 12.3514498 249.3100
stl 1994 Mar 193.5068 234.7259 -24.0197102 -17.1994480 217.5265
stl 1994 Apr 223.6958 232.4933 4.3207573 -13.1182838 219.3750
stl 1994 May 243.1989 230.9541 2.7982619 9.4465107 240.4007
stl 1994 Jun 194.8713 229.4150 -3.9574642 -30.5862471 198.8288
stl 1994 Jul 217.8992 227.8758 19.1401570 -29.1168166 198.7590
stl 1994 Aug 214.3996 227.2761 -8.6991989 -4.1772690 223.0988
stl 1994 Sep 241.8272 226.6764 14.8789318 0.2718847 226.9483
stl 1994 Oct 191.7426 226.0766 -18.7928666 -15.5411836 210.5354
stl 1994 Nov 290.0108 228.0993 -3.6014482 65.5129579 293.6122
stl 1994 Dec 182.1188 230.1220 -14.7846331 -33.2185134 196.9034
stl 1995 Jan 208.2682 232.1446 -2.9742823 -20.9021161 211.2425
stl 1995 Feb 273.2187 232.6135 36.7505397 3.8547036 236.4682
stl 1995 Mar 207.1053 233.0823 -18.4057825 -7.5712388 225.5111
stl 1995 Apr 229.3843 233.5512 5.8691095 -10.0359563 223.5152
stl 1995 May 313.1791 234.0890 7.5669228 71.5232371 305.6122
stl 1995 Jun 236.0774 234.6267 -4.6425529 6.0932298 240.7200
stl 1995 Jul 256.7147 235.1645 5.5860249 15.9641428 251.1286
stl 1995 Aug 191.4221 238.8203 -6.0716982 -41.3264916 197.4938
stl 1995 Sep 217.4239 242.4762 18.6893945 -43.7416124 198.7345
stl 1995 Oct 191.0621 246.1320 -29.8576698 -25.2122126 220.9198
stl 1995 Nov 263.6238 247.9719 -2.9102688 18.5621600 266.5340
stl 1995 Dec 181.4527 249.8118 -10.0913510 -58.2676574 191.5441
stl 1996 Jan 226.5905 251.6516 -2.6193419 -22.4418352 229.2098
stl 1996 Feb 359.7138 252.3350 35.1835692 72.1952334 324.5302
stl 1996 Mar 299.2565 253.0183 -14.3397376 60.5779619 313.5963
stl 1996 Apr 331.0153 253.7016 9.0273100 68.2863575 321.9880
stl 1996 May 255.0153 253.7756 0.4852327 0.7544502 254.5301
stl 1996 Jun 232.0018 253.8496 -3.9626437 -17.8851595 235.9644
stl 1996 Jul 229.3879 253.9236 -6.5423477 -17.9933016 235.9303
stl 1996 Aug 222.4743 251.5877 -6.3637359 -22.7495876 228.8381
stl 1996 Sep 261.8056 249.2518 25.2825576 -12.7287308 236.5230
stl 1996 Oct 199.0621 246.9158 -27.3455376 -20.5081929 226.4076
stl 1996 Nov 186.8065 245.5475 1.2420035 -59.9830223 185.5645
stl 1996 Dec 269.8668 244.1792 -3.0046652 28.6922895 272.8715
stl 1997 Jan 288.8191 242.8108 -3.3153664 49.3236232 292.1344
stl 1997 Feb 279.6058 243.9618 32.6451650 2.9987648 246.9606
stl 1997 Mar 241.2115 245.1128 -11.1655952 7.2642799 252.3771
stl 1997 Apr 245.8812 246.2638 11.4576834 -11.8403374 234.4235
stl 1997 May 236.1422 244.9302 -7.1602093 -1.6277672 243.3024
stl 1997 Jun 211.0045 243.5965 -3.6537581 -28.9382807 214.6583
stl 1997 Jul 229.8812 242.2629 -18.8490157 6.4673160 248.7302
stl 1997 Aug 300.5779 239.4410 -6.6632880 67.8001515 307.2411
stl 1997 Sep 280.1062 236.6191 32.0389871 11.4481227 248.0672
stl 1997 Oct 193.5068 233.7972 -24.5528902 -15.7375664 218.0596
stl 1997 Nov 223.6958 232.3286 5.7920394 -14.4248539 217.9037
stl 1997 Dec 243.1989 230.8600 4.5285337 7.8104253 238.6704
stl 1998 Jan 194.8713 229.3913 -3.9869826 -30.5330680 198.8583
stl 1998 Feb 217.8992 228.0479 19.0567115 -29.2054043 198.8425
stl 1998 Mar 214.3996 226.7044 -8.7192481 -3.5855397 223.1189
stl 1998 Apr 241.8272 225.3610 14.9344963 1.5317136 226.8927
stl 1998 May 191.7426 227.1044 -18.6119741 -16.7498416 210.3545
stl 1998 Jun 290.0108 228.8478 -3.4038060 64.5667999 293.4146
stl 1998 Jul 182.1188 230.5912 -14.5882967 -33.8841158 196.7071
stl 1998 Aug 208.2682 231.7649 -3.5000495 -19.9966441 211.7683
stl 1998 Sep 273.2187 232.9386 35.0540897 5.2260158 238.1646
stl 1998 Oct 207.1053 234.1123 -19.2247745 -7.7822273 226.3301
stl 1998 Nov 229.3843 233.9883 6.7424232 -11.3463837 222.6419
stl 1998 Dec 313.1791 233.8643 4.5236818 74.7911505 308.6554
stl 1999 Jan 236.0774 233.7403 -4.3740953 6.7112308 240.4515
stl 1999 Feb 256.7147 236.6556 5.7297543 14.3293468 250.9849
stl 1999 Mar 191.4221 239.5709 -6.0344119 -42.1143145 197.4566
stl 1999 Apr 217.4239 242.4862 18.5854478 -43.6476722 198.8385
stl 1999 May 191.0621 245.0891 -29.9539509 -24.0730364 221.0161
stl 1999 Jun 263.6238 247.6920 -3.1488763 19.0806185 266.7726
stl 1999 Jul 181.4527 250.2949 -10.4274105 -58.4147910 191.8802
stl 1999 Aug 226.5905 251.0879 -0.5669495 -23.9304877 227.1574
stl 1999 Sep 359.7138 251.8808 37.7087482 70.1241775 322.0050
stl 1999 Oct 299.2565 252.6738 -14.3723587 60.9550892 313.6289
stl 1999 Nov 331.0153 253.1732 7.1018511 70.7402295 323.9135
stl 1999 Dec 255.0153 253.6726 3.8694543 -2.5267994 251.1458
stl 2000 Jan 232.0018 254.1721 -4.2962628 -17.8740094 236.2981
stl 2000 Feb 229.3879 252.8270 -6.7644357 -16.6746123 236.1524
stl 2000 Mar 222.4743 251.4819 -6.5663668 -22.4411870 229.0407
stl 2000 Apr 261.8056 250.1368 25.1134893 -13.4447246 236.6921
stl 2000 May 199.0621 247.6816 -27.3692892 -21.2501902 226.4314
stl 2000 Jun 186.8065 245.2264 1.2991657 -59.7190404 185.5073
stl 2000 Jul 269.8668 242.7711 -2.8827917 29.9784531 272.7496
stl 2000 Aug 288.8191 243.7369 -3.6984880 48.7806461 292.5176
stl 2000 Sep 279.6058 244.7027 29.8626929 5.0403453 249.7431
stl 2000 Oct 241.2115 245.6685 -10.4012487 5.9442489 251.6128
stl 2000 Nov 245.8812 245.4185 11.3632512 -10.9005447 234.5179
stl 2000 Dec 236.1422 245.1684 -8.0689408 -0.9572873 244.2112
stl 2001 Jan 211.0045 244.9184 -3.4381406 -30.4757619 214.4426
stl 2001 Feb 229.8812 241.9417 -18.5332165 6.4726775 248.4144
stl 2001 Mar 300.5779 238.9651 -6.4277930 68.0405994 307.0057
stl 2001 Apr 280.1062 235.9884 32.1713253 11.9465097 247.9349
stl 2001 May 193.5068 234.2662 -24.3955673 -16.3638663 217.9023
stl 2001 Jun 223.6958 232.5440 5.9559459 -14.8041693 217.7398
stl 2001 Jul 243.1989 230.8218 4.6902436 7.6868747 238.5087
stl 2001 Aug 194.8713 229.2308 -6.9689447 -27.3905211 201.8402
stl 2001 Sep 217.8992 227.6397 21.7103845 -31.4508990 196.1888
stl 2001 Oct 214.3996 226.0487 -6.8500944 -4.7989214 221.2497
stl 2001 Nov 241.8272 226.7738 15.0909926 -0.0376215 226.7362
stl 2001 Dec 191.7426 227.4990 -20.5670567 -15.1893365 212.3096
stl 2002 Jan 290.0108 228.2241 -3.4836714 65.2703493 293.4945
stl 2002 Feb 182.1188 230.0468 -14.5979701 -33.3300062 196.7168
stl 2002 Mar 208.2682 231.8695 -3.5596786 -20.0415478 211.8279
stl 2002 Apr 273.2187 233.6921 34.9368528 4.5897509 238.2819
stl 2002 May 207.1053 233.6027 -19.4089263 -7.0884411 226.5142
stl 2002 Jun 229.3843 233.5132 6.5737755 -10.7026747 222.8106
stl 2002 Jul 313.1791 233.4238 4.3750008 75.3803198 308.8041
stl 2002 Aug 236.0774 235.0562 -4.4285830 5.4497596 240.5060
stl 2002 Sep 256.7147 236.6887 5.3305065 14.6955002 251.3842
stl 2002 Oct 191.4221 238.3211 -7.6787767 -39.2201796 199.1009
stl 2002 Nov 217.4239 241.6421 19.6783900 -43.8965276 197.7456
stl 2002 Dec 191.0621 244.9631 -25.3838913 -28.5170639 216.4460
stl 2003 Jan 263.6238 248.2840 -3.3976577 18.7373772 267.0214
stl 2003 Feb 181.4527 249.4680 -10.5586916 -57.4565237 192.0114
stl 2003 Mar 226.5905 250.6519 -0.6150446 -23.4463746 227.2055
stl 2003 Apr 359.7138 251.8358 37.7701637 70.1078118 321.9436
stl 2003 May 299.2565 252.6209 -14.3632379 60.9988890 313.6198
stl 2003 Jun 331.0153 253.4060 7.2789478 70.3304004 323.7364
stl 2003 Jul 255.0153 254.1910 4.1753962 -3.3511267 250.8399
stl 2003 Aug 232.0018 253.7320 -1.7084651 -20.0217300 233.7103
stl 2003 Sep 229.3879 253.2730 -10.8054976 -13.0795222 240.1934
stl 2003 Oct 222.4743 252.8139 -8.1911693 -22.1484052 230.6655
stl 2003 Nov 261.8056 250.0534 24.6544929 -12.9022730 237.1511
stl 2003 Dec 199.0621 247.2928 -29.7651174 -18.4655759 228.8272
stl 2004 Jan 186.8065 244.5322 1.6324060 -59.3581638 185.1741
stl 2004 Feb 269.8668 244.4726 -2.6387403 28.0328963 272.5055
stl 2004 Mar 288.8191 244.4130 -3.4706456 47.8767047 292.2897
stl 2004 Apr 279.6058 244.3534 30.0573396 5.1950059 249.5484
stl 2004 May 241.2115 244.9053 -10.3660642 6.6722408 251.5776
stl 2004 Jun 245.8812 245.4573 11.3317607 -10.9078465 234.5494
stl 2004 Jul 236.1422 246.0092 -8.1461794 -1.7208098 244.2884
stl 2004 Aug 211.0045 243.6307 -3.3849830 -29.2412433 214.3895
stl 2004 Sep 229.8812 241.2523 -14.2199272 2.8488651 244.1011
stl 2004 Oct 300.5779 238.8738 -5.6290677 67.3331519 306.2069
stl 2004 Nov 280.1062 236.6052 30.5847268 12.9162625 249.5215
stl 2004 Dec 193.5068 234.3367 -24.2403756 -16.5895430 217.7471
stl 2005 Jan 223.6958 232.0681 5.8214653 -14.1938129 217.8743
stl 2005 Feb 243.1989 230.6456 4.4856823 8.0676833 238.7132
stl 2005 Mar 194.8713 229.2230 -7.0762997 -27.2754047 201.9476
stl 2005 Apr 217.8992 227.8004 21.7240662 -31.6253050 196.1751
stl 2005 May 214.3996 227.2941 -6.8597361 -6.0347405 221.2594
stl 2005 Jun 241.8272 226.7878 15.0653060 -0.0259277 226.7619
stl 2005 Jul 191.7426 226.2815 -20.6154445 -13.9234734 212.3580
stl 2005 Aug 290.0108 228.3911 -5.0418066 66.6615218 295.0526
stl 2005 Sep 182.1188 230.5007 -17.4472787 -30.9345890 199.5661
stl 2005 Oct 208.2682 232.6103 -2.7588878 -21.5831586 211.0271
stl 2005 Nov 273.2187 233.0261 36.9440391 3.2486025 236.2747
stl 2005 Dec 207.1053 233.4419 -18.2377449 -8.0988320 225.3431
stl 2006 Jan 229.3843 233.8577 6.6094801 -11.0828361 222.7749
stl 2006 Feb 313.1791 234.2395 4.3102320 74.6294219 308.8689
stl 2006 Mar 236.0774 234.6212 -4.4531657 5.9093398 240.5306
stl 2006 Apr 256.7147 235.0030 5.3552536 16.3564147 251.3594
stl 2006 May 191.4221 238.5943 -7.5982083 -39.5739083 199.0204
stl 2006 Jun 217.4239 242.1855 19.7455559 -44.5071279 197.6784
stl 2006 Jul 191.0621 245.7768 -25.3269985 -29.3876653 216.3891
stl 2006 Aug 263.6238 247.5877 -1.2623291 17.2983996 264.8861
stl 2006 Sep 181.4527 249.3986 -9.7406103 -58.2052582 191.1934
stl 2006 Oct 226.5905 251.2095 -2.9215392 -21.6975373 229.5120
stl 2006 Nov 359.7138 252.0271 34.9271512 72.7595447 324.7866
stl 2006 Dec 299.2565 252.8446 -14.5423451 60.9542555 313.7989
stl 2007 Jan 331.0153 253.6622 7.4439970 69.9091494 323.5713
stl 2007 Feb 255.0153 253.8419 4.2049315 -3.0314929 250.8104
stl 2007 Mar 232.0018 254.0216 -1.7362343 -20.2835364 233.7380
stl 2007 Apr 229.3879 254.2013 -10.9051825 -13.9081574 240.2931
stl 2007 May 222.4743 251.8736 -8.2137249 -21.1855663 230.6881
stl 2007 Jun 261.8056 249.5460 24.5336636 -12.2740816 237.2719
stl 2007 Jul 199.0621 247.2184 -29.9457926 -18.2104597 229.0079
stl 2007 Aug 186.8065 245.7886 2.5569257 -61.5390901 184.2496
stl 2007 Sep 269.8668 244.3589 -2.0471473 27.5550023 271.9139
stl 2007 Oct 288.8191 242.9292 -3.1662585 49.0561223 291.9853
stl 2007 Nov 279.6058 243.9557 32.7593329 2.8907144 246.8464
stl 2007 Dec 241.2115 244.9822 -11.0627111 7.2920239 252.2742
stl 2008 Jan 245.8812 246.0087 11.1724889 -11.3000043 234.7087
stl 2008 Feb 236.1422 244.6953 -8.2539894 -0.2990866 244.3962
stl 2008 Mar 211.0045 243.3819 -3.4750168 -28.9023596 214.4795
stl 2008 Apr 229.8812 242.0685 -14.2815598 2.0942845 244.1627
stl 2008 May 300.5779 239.2889 -5.5066732 66.7956286 306.0845
stl 2008 Jun 280.1062 236.5093 30.7367394 12.8601298 249.3695
stl 2008 Jul 193.5068 233.7298 -24.0738424 -16.1491873 217.5806
stl 2008 Aug 223.6958 232.3750 4.2896132 -12.9688050 219.4062
stl 2008 Sep 243.1989 231.0201 2.8946720 9.2841055 240.3042
stl 2008 Oct 194.8713 229.6653 -3.7318877 -31.0621485 198.6032
stl 2008 Nov 217.8992 228.3670 19.3186305 -29.7864801 198.5806
stl 2008 Dec 214.3996 227.0688 -8.4684389 -4.2006769 222.8681
stl 2009 Jan 241.8272 225.7705 15.2543727 0.8023382 226.5728
stl 2009 Feb 191.7426 227.4293 -20.3900293 -15.2966495 212.1326
stl 2009 Mar 290.0108 229.0880 -4.9214294 65.8441964 294.9322
stl 2009 Apr 182.1188 230.7468 -17.4602134 -31.1677900 199.5790
stl 2009 May 208.2682 231.8298 -2.6965438 -20.8650123 210.9648
stl 2009 Jun 273.2187 232.9128 36.9115164 3.3944548 236.3072
stl 2009 Jul 207.1053 233.9957 -18.3615678 -8.5288401 225.4669
stl 2009 Aug 229.3843 233.7308 5.7316225 -10.0780945 223.6527
stl 2009 Sep 313.1791 233.4659 7.4148105 72.2984050 305.7643
stl 2009 Oct 236.0774 233.2010 -4.8057663 7.6821797 240.8832
stl 2009 Nov 256.7147 236.1601 5.2831102 15.2715088 251.4316
stl 2009 Dec 191.4221 239.1191 -6.4728908 -41.2240775 197.8950
stl 2010 Jan 217.4239 242.0782 19.4987735 -44.1529997 197.9252
stl 2010 Feb 191.0621 244.7991 -25.4916638 -28.2453720 216.5538
stl 2010 Mar 263.6238 247.5201 -1.4455355 17.5491825 265.0693
stl 2010 Apr 181.4527 250.2411 -9.9395473 -58.8487963 191.3923
stl 2010 May 226.5905 251.1386 -3.1130630 -21.4350391 229.7035
stl 2010 Jun 359.7138 252.0360 34.7737873 72.9039506 324.9400
stl 2010 Jul 299.2565 252.9335 -14.6655802 60.9886001 313.9221
stl 2010 Aug 331.0153 253.5118 8.7093944 68.7940804 322.3059
stl 2010 Sep 255.0153 254.0901 0.2605726 0.6645811 254.7547
stl 2010 Oct 232.0018 254.6685 -4.0969099 -18.5697587 236.0987
stl 2010 Nov 229.3879 253.2062 -6.5646066 -17.2536618 235.9525
stl 2010 Dec 222.4743 251.7439 -6.3794210 -22.8901773 228.8538
stl 2011 Jan 261.8056 250.2817 24.3899110 -12.8660146 237.4157
stl 2011 Feb 199.0621 247.7153 -30.0261652 -18.6270017 229.0883
stl 2011 Mar 186.8065 245.1489 2.5178879 -60.8602693 184.2886
stl 2011 Apr 269.8668 242.5825 -2.0423022 29.3266380 271.9091
stl 2011 May 288.8191 243.5156 -3.2639540 48.5674343 292.0830
stl 2011 Jun 279.6058 244.4488 32.8025543 2.3544540 246.8032
stl 2011 Jul 241.2115 245.3819 -10.9022289 6.7318471 252.1138
stl 2011 Aug 245.8812 245.1708 11.6963606 -10.9859810 234.1848
stl 2011 Sep 236.1422 244.9597 -6.9426404 -1.8748595 243.0849
stl 2011 Oct 211.0045 244.7486 -3.4587815 -30.2853378 214.4633
stl 2011 Nov 229.8812 241.8861 -18.5048039 6.4999045 248.3860
stl 2011 Dec 300.5779 239.0236 -6.3763407 67.9306431 306.9542
stl 2012 Jan 280.1062 236.1610 30.8519979 13.0931895 249.2542
stl 2012 Feb 193.5068 234.4862 -23.9715258 -17.0079682 217.4783
stl 2012 Mar 223.6958 232.8115 4.3799663 -13.4956629 219.3158
stl 2012 Apr 243.1989 231.1367 2.9573532 9.1048791 240.2416
stl 2012 May 194.8713 229.4977 -3.8643169 -30.7621031 198.7356
stl 2012 Jun 217.8992 227.8587 19.1647420 -29.1242787 198.7344
stl 2012 Jul 214.3996 226.2197 -8.6258528 -3.1942534 223.0255
stl 2012 Aug 241.8272 226.8305 14.9710244 0.0256111 226.8562
stl 2012 Sep 191.7426 227.4413 -18.6873611 -17.0114129 210.4299
stl 2012 Oct 290.0108 228.0521 -3.5869746 65.5456263 293.5978
stl 2012 Nov 182.1188 229.7963 -14.7409240 -32.9365953 196.8597
stl 2012 Dec 208.2682 231.5405 -3.7224873 -19.5497989 211.9907
stl 2013 Jan 273.2187 233.2847 36.7525977 3.1814292 236.4661
stl 2013 Feb 207.1053 233.2465 -18.4164930 -7.7247149 225.5218
stl 2013 Mar 229.3843 233.2083 5.8043188 -9.6283223 223.5800
stl 2013 Apr 313.1791 233.1702 7.6498570 72.3590956 305.5293
stl 2013 May 236.0774 234.9093 -4.6412571 5.8093659 240.7187
stl 2013 Jun 256.7147 236.6484 5.5185306 14.5477083 251.1961
stl 2013 Jul 191.4221 238.3876 -6.1896974 -40.7757265 197.6118
stl 2013 Aug 217.4239 241.8420 18.5711646 -42.9891766 198.8528
stl 2013 Sep 191.0621 245.2963 -29.9409083 -24.2933279 221.0030
stl 2013 Oct 263.6238 248.7507 -3.1131075 17.9861393 266.7369
stl 2013 Nov 181.4527 249.9368 -10.2640972 -58.2200075 191.7168
stl 2013 Dec 226.5905 251.1230 -0.3402731 -24.1922372 226.9307
stl 2014 Jan 359.7138 252.3091 35.0637981 72.3408845 324.6500
stl 2014 Feb 299.2565 252.9505 -14.4939441 60.7999875 313.7505
stl 2014 Mar 331.0153 253.5919 8.8513435 68.5720823 322.1640
stl 2014 Apr 255.0153 254.2333 0.3750872 0.4069451 254.6402
stl 2014 May 232.0018 253.6625 -4.0451245 -17.6155876 236.0469
stl 2014 Jun 229.3879 253.0918 -6.5954543 -17.1083621 235.9834
stl 2014 Jul 222.4743 252.5210 -6.4795424 -23.5671085 228.9539
stl 2014 Aug 261.8056 249.6874 25.2345399 -13.1163750 236.5710
stl 2014 Sep 199.0621 246.8538 -27.3300973 -20.4616297 226.3922
stl 2014 Oct 186.8065 244.0203 1.2619338 -58.4757037 185.5445
stl 2014 Nov 269.8668 244.0423 -3.0050130 28.8295229 272.8718
stl 2014 Dec 288.8191 244.0643 -3.8112839 48.5660629 292.6304
stl 2015 Jan 279.6058 244.0863 32.7841102 2.7353213 246.8217
stl 2015 Feb 241.2115 244.7492 -11.0543185 7.5166554 252.2658
stl 2015 Mar 245.8812 245.4120 11.5234102 -11.0542614 234.3578
stl 2015 Apr 236.1422 246.0749 -7.1295209 -2.8031594 243.2717
stl 2015 May 211.0045 243.7654 -3.5337104 -29.2272070 214.5382
stl 2015 Jun 229.8812 241.4559 -18.6527127 7.0779597 248.5339
stl 2015 Jul 300.5779 239.1465 -6.5712156 68.0026089 307.1491
stl 2015 Aug 280.1062 236.8890 32.1977809 11.0194696 247.9084
stl 2015 Sep 193.5068 234.6315 -24.3177264 -16.8069789 217.8245
stl 2015 Oct 223.6958 232.3740 6.0790168 -14.7571990 217.6168
stl 2015 Nov 243.1989 230.8357 4.7365949 7.6266035 238.4623
stl 2015 Dec 194.8713 229.2975 -6.8265645 -27.5996397 201.6979
stl 2016 Jan 217.8992 227.7593 19.2894866 -29.1495578 198.6097
stl 2016 Feb 214.3996 227.2352 -8.5048655 -4.3306597 222.9045
stl 2016 Mar 241.8272 226.7111 15.1182689 -0.0021555 226.7089
stl 2016 Apr 191.7426 226.1870 -18.5139116 -15.9304877 210.2565
stl 2016 May 290.0108 228.2721 -3.2731663 65.0118973 293.2840
stl 2016 Jun 182.1188 230.3572 -14.4262054 -33.8121494 196.5450
stl 2016 Jul 208.2682 232.4423 -3.4266544 -20.7473821 211.6949
stl 2016 Aug 273.2187 232.9340 35.1039279 5.1808169 238.1148
stl 2016 Sep 207.1053 233.4257 -19.1973023 -7.1230782 226.3026
stl 2016 Oct 229.3843 233.9174 6.8274832 -11.3605497 222.5569
stl 2016 Nov 313.1791 234.4363 4.5333450 74.2094824 308.6458
stl 2016 Dec 236.0774 234.9552 -4.2426746 5.3649061 240.3201
stl 2017 Jan 256.7147 235.4741 5.6509568 15.5896528 251.0637
stl 2017 Feb 191.4221 239.0450 -6.1434913 -41.4793284 197.5656
stl 2017 Mar 217.4239 242.6159 18.4808764 -43.6727959 198.9431
stl 2017 Apr 191.0621 246.1868 -30.2132594 -24.9113962 221.2754
stl 2017 May 263.6238 247.8850 -3.4102854 19.1490241 267.0340
stl 2017 Jun 181.4527 249.5833 -10.7152780 -57.4152622 192.1680
stl 2017 Jul 226.5905 251.2815 -0.9155896 -23.7754986 227.5060
stl 2017 Aug 359.7138 251.8838 37.2532290 70.5767623 322.4605
stl 2017 Sep 299.2565 252.4860 -14.9570736 61.7275864 314.2136
stl 2017 Oct 331.0153 253.0882 6.6183571 71.3086988 324.3969
stl 2017 Nov 255.0153 253.2582 3.2951054 -1.5379616 251.7202
stl 2017 Dec 232.0018 253.4281 -2.6841554 -18.7421144 234.6860
stl 2018 Jan 229.3879 253.5980 -2.6618638 -21.5481795 232.0498
stl 2018 Feb 222.4743 251.4491 -5.5628996 -23.4118413 228.0372
stl 2018 Mar 261.8056 249.3002 24.4695692 -11.9641831 237.3360
stl 2018 Apr 199.0621 247.1513 -26.3699895 -21.7192049 225.4321
stl 2018 May 186.8065 245.8055 0.5123275 -59.5113942 186.2942
stl 2018 Jun 269.8668 244.4598 -6.0707518 31.4777444 275.9375
stl 2018 Jul 288.8191 243.1140 -4.6325256 50.3375668 293.4516
stl 2018 Aug 279.6058 244.1711 29.7694753 5.6651668 249.8363
stl 2018 Sep 241.2115 245.2282 -12.1262883 8.1096132 253.3378
stl 2018 Oct 245.8812 246.2853 8.4660187 -8.8701046 237.4152
stl 2018 Nov 236.1422 244.8947 -6.2142869 -2.5382072 242.3565
stl 2018 Dec 211.0045 243.5041 -5.2576983 -27.2419438 216.2622
stl 2019 Jan 229.8812 242.1136 -9.8028085 -2.4295803 239.6840
stl 2019 Feb 300.5779 239.2450 -3.8552259 65.1881159 304.4331
stl 2019 Mar 280.1062 236.3764 31.5405500 12.1893021 248.5657
stl 2019 Apr 193.5068 233.5077 -21.5461828 -18.4548158 215.0529
stl 2019 May 223.6958 232.1246 5.3137259 -13.7425945 218.3820
stl 2019 Jun 243.1989 230.7415 -0.6623581 13.1197509 243.8613
stl 2019 Jul 194.8713 229.3584 -7.7005121 -26.7866168 202.5718
stl 2019 Aug 217.8992 228.1771 22.8367400 -33.1146239 195.0624
stl 2019 Sep 214.3996 226.9957 -8.8424160 -3.7536758 223.2421
stl 2019 Oct 241.8272 225.8144 10.7068732 5.3059198 231.1203
stl 2019 Nov 191.7426 227.5072 -15.3903802 -20.3742709 207.1330
stl 2019 Dec 290.0108 229.2001 -7.5238139 68.3345538 297.5346
stl 2020 Jan 182.1188 230.8929 -10.9809950 -37.7930900 193.0998
stl 2020 Feb 208.2682 231.8855 -2.3121892 -21.3050863 210.5804
stl 2020 Mar 273.2187 232.8781 33.7303388 6.6102752 239.4884
stl 2020 Apr 207.1053 233.8707 -20.0968052 -6.6685976 227.2021
stl 2020 May 229.3843 233.7096 6.2827979 -10.6080474 223.1015
stl 2020 Jun 313.1791 233.5485 1.3290552 78.3016001 311.8501
stl 2020 Jul 236.0774 233.3873 -8.4390612 11.1291317 244.5165
stl 2020 Aug 256.7147 236.4328 20.7625561 -0.4806447 235.9521
stl 2020 Sep 191.4221 239.4782 -7.3291328 -40.7269080 198.7513
stl 2020 Oct 217.4239 242.5236 11.5189730 -36.6186365 205.9050
stl 2020 Nov 191.0621 245.0921 -18.3654140 -35.6645733 209.4275
stl 2020 Dec 263.6238 247.6606 -7.8370129 23.8001942 271.4608
stl 2021 Jan 181.4527 250.2291 -12.5776456 -56.1986777 194.0304
stl 2021 Feb 226.5905 250.9887 -1.1868039 -23.2114106 227.7773
stl 2021 Mar 359.7138 251.7483 35.5032893 72.4622037 324.2105
stl 2021 Apr 299.2565 252.5079 -19.0321076 65.7807500 318.2886
stl 2021 May 331.0153 253.2083 6.8993483 70.9076230 324.1160
stl 2021 Jun 255.0153 253.9088 3.0201708 -1.9136466 251.9951
stl 2021 Jul 232.0018 254.6092 -9.4256840 -13.1817402 241.4275
stl 2021 Aug 229.3879 253.2780 18.4983819 -42.3884627 210.8896
stl 2021 Sep 222.4743 251.9468 -5.9477566 -23.5247110 228.4221
stl 2021 Oct 261.8056 250.6156 12.2441147 -1.0541445 249.5615
stl 2021 Nov 199.0621 247.9098 -21.3824570 -27.4651925 220.4446
stl 2021 Dec 186.8065 245.2039 -8.1676711 -50.2297494 194.9742
stl 2022 Jan 269.8668 242.4980 -13.8848167 41.2535569 283.7516
stl 2022 Feb 288.8191 243.0226 -0.5101998 46.3067212 289.3293
stl 2022 Mar 279.6058 243.5471 37.0656026 -1.0069165 242.5402
stl 2022 Apr 241.2115 244.0716 -18.0366258 15.1765584 259.2481
stl 2022 May 245.8812 244.2974 7.5236964 -5.9398737 238.3575
stl 2022 Jun 236.1422 244.5231 4.4990157 -12.8799437 231.6432
stl 2022 Jul 211.0045 244.7489 -10.0314772 -23.7129414 221.0360
stl 2022 Aug 229.8812 244.6708 16.8198883 -31.6094839 213.0613
stl 2022 Sep 300.5779 244.5926 -5.5207510 61.5059605 306.0986
stl 2022 Oct 280.1062 244.5145 12.4177462 23.1739515 267.6885
stl 2022 Nov 193.5068 244.3391 -23.5319477 -27.3004254 217.0387
stl 2022 Dec 223.6958 244.1637 -8.3302205 -12.1377447 232.0260
components(dcmp) |>
  as_tsibble() |>
  autoplot(value, colour="blue") +
  geom_line(aes(y=trend), colour = "#D55E00") +
  labs(
    y = "Sea Ice Concentration",
    title = "Serie de tiempo descompuesta de Sea Ice Cover en 48.1"
  ) +
  theme_bw()

Ahora lo descompongo en los demas componentes

components(dcmp) |> 
  autoplot(colour="blue") +
  theme_bw()

Model ARIMA

train <- dtats$meansic[1:40]
test <- dtats$meansic[40:43]

model1 <- arima(train, order =c(1,2,1))

predo <- forecast::forecast(model1, h=10)
plot(predo)

Moving Average.

mov_avg <- zoo::rollmean(dtats1$meansic, k=3, fill=NA)


prediction <- tail(mov_avg, n=2)

ggplot() + 
  geom_line(aes(x = as.double(dtats1$ANO), y = dtats1$meansic), 
            data = dtats, color = "blue") +
  geom_line(aes(x = as.double(dtats1$ANO), y = mov_avg), 
            data =dtats, color = "red") +
  geom_hline(yintercept = prediction, color = "green") +
  xlab("Fecha") +
  ylab("Datos") +
  ggtitle("Datos y media móvil") +
  theme_bw()

Time Series TSM

Now, we use meantsm variable

Change dtats1 from data.frameto ts object.

dtats2 <- dtats1 %>% 
  filter(ANOn>1990) %>% 
  mutate(meantsm2=meantsm-270)
ts_tsm <- ts(dtats2$meantsm2, 
             start = c(dtats2$ANOn[1], 1),
             end = c(dtats2$ANOn[length(dtats2$ANOn)], 12),
             frequency = 12)

ts_tsm2 <- as_tsibble(ts_tsm)

A subseries plot to show difference.

ts_tsm2 |>
  gg_subseries(value) +
  labs(
    y = "TSM",
    title = "TSM SubArea 48.1"
  )+
  theme_bw()

### Autocorrelacion

An scaterplot of correlation simple bettwen lags. We select 60 lags, to get entire series of SIC.

ts_tsm2 %>% 
  gg_lag(value, 
         geom="point",
         lags = 1:12)

ts_tsm2 |> 
  ACF(value, lag_max = 60) %>% 
  autoplot() +
  labs(title = "Autocorrelacion de TSM in 48.1")+
  theme_bw()

We then describe a trend correlation and also a seasonal one, which is very characteristic of environmental data.

Descomposicion

In this chapter, we consider the most common methods for extracting these components from a time series. Often this is done to help improve understanding of the time series, but it can also be used to improve forecast accuracy.

When decomposing a time series, it is sometimes helpful to first transform or adjust the series in order to make the decomposition (and later analysis) as simple as possible. So we will begin by discussing transformations and adjustments.

dcmptsm <- ts_tsm2|>
  model(stl = STL(value))
kableExtra::kable(components(dcmptsm))
.model index value trend season_year remainder season_adjust
stl 1991 Jan 2.432902 2.532919 -0.0602236 -0.0397927 2.493126
stl 1991 Feb 2.445528 2.546423 -0.0197455 -0.0811490 2.465274
stl 1991 Mar 2.720644 2.559927 0.0710816 0.0896351 2.649562
stl 1991 Apr 2.562643 2.573431 0.0574606 -0.0682482 2.505183
stl 1991 May 2.534155 2.585316 -0.0175698 -0.0335915 2.551725
stl 1991 Jun 2.669778 2.597201 0.0445836 0.0279933 2.625195
stl 1991 Jul 2.642216 2.609086 0.0366087 -0.0034783 2.605608
stl 1991 Aug 2.682374 2.620459 -0.0054927 0.0674079 2.687867
stl 1991 Sep 2.727599 2.631832 -0.0611128 0.1568790 2.788711
stl 1991 Oct 2.746914 2.643206 -0.0317938 0.1355021 2.778708
stl 1991 Nov 2.628667 2.649780 0.0134566 -0.0345695 2.615210
stl 1991 Dec 2.524138 2.656353 -0.0240238 -0.1081919 2.548162
stl 1992 Jan 2.656771 2.662927 -0.0565043 0.0503477 2.713275
stl 1992 Feb 2.593845 2.657000 -0.0141797 -0.0489760 2.608024
stl 1992 Mar 2.507135 2.651073 0.0687324 -0.2126709 2.438402
stl 1992 Apr 2.894904 2.645146 0.0519899 0.1977676 2.842914
stl 1992 May 2.713364 2.629813 -0.0224474 0.1059982 2.735812
stl 1992 Jun 2.721785 2.614480 0.0369461 0.0703588 2.684839
stl 1992 Jul 2.721577 2.599148 0.0349827 0.0874470 2.686594
stl 1992 Aug 2.528965 2.592779 -0.0050027 -0.0588121 2.533968
stl 1992 Sep 2.581207 2.586412 -0.0605874 0.0553826 2.641794
stl 1992 Oct 2.625677 2.580043 -0.0288227 0.0744559 2.654499
stl 1992 Nov 2.446975 2.586147 0.0177383 -0.1569103 2.429237
stl 1992 Dec 2.283491 2.592251 -0.0187286 -0.2900309 2.302220
stl 1993 Jan 2.332737 2.598354 -0.0529584 -0.2126584 2.385696
stl 1993 Feb 2.355041 2.607405 -0.0087785 -0.2435860 2.363819
stl 1993 Mar 2.897337 2.616457 0.0662272 0.2146535 2.831110
stl 1993 Apr 2.761315 2.625508 0.0463926 0.0894149 2.714923
stl 1993 May 2.679809 2.636330 -0.0274221 0.0709015 2.707231
stl 1993 Jun 2.887291 2.647152 0.0292695 0.2108689 2.858021
stl 1993 Jul 2.836600 2.657974 0.0333759 0.1452498 2.803224
stl 1993 Aug 2.921793 2.662449 -0.0044106 0.2637539 2.926203
stl 1993 Sep 2.432902 2.666924 -0.0598770 -0.1741450 2.492779
stl 1993 Oct 2.445528 2.671399 -0.0255864 -0.2002846 2.471115
stl 1993 Nov 2.720644 2.663626 0.0223657 0.0346520 2.698278
stl 1993 Dec 2.562643 2.655853 -0.0130262 -0.0801831 2.575670
stl 1994 Jan 2.534155 2.648080 -0.0471364 -0.0667884 2.581291
stl 1994 Feb 2.669778 2.643272 0.0019166 0.0245894 2.667861
stl 1994 Mar 2.642216 2.638465 0.0615100 -0.0577583 2.580706
stl 1994 Apr 2.682374 2.633657 0.0355647 0.0131524 2.646810
stl 1994 May 2.727599 2.640204 -0.0354995 0.1228944 2.763098
stl 1994 Jun 2.746914 2.646750 0.0156220 0.0845418 2.731292
stl 1994 Jul 2.628667 2.653296 0.0314589 -0.0560886 2.597208
stl 1994 Aug 2.524138 2.655712 -0.0026339 -0.1289407 2.526772
stl 1994 Sep 2.656771 2.658128 -0.0618893 0.0605318 2.718660
stl 1994 Oct 2.593845 2.660544 -0.0231900 -0.0435097 2.617035
stl 1994 Nov 2.507135 2.650729 0.0318834 -0.1754780 2.475251
stl 1994 Dec 2.894904 2.640914 0.0023431 0.2516463 2.892561
stl 1995 Jan 2.713364 2.631099 -0.0417409 0.1240059 2.755105
stl 1995 Feb 2.721785 2.617119 0.0121915 0.0924750 2.709594
stl 1995 Mar 2.721577 2.603139 0.0563788 0.0620598 2.665198
stl 1995 Apr 2.528965 2.589158 0.0244566 -0.0846501 2.504508
stl 1995 May 2.581207 2.586602 -0.0437229 0.0383277 2.624930
stl 1995 Jun 2.625677 2.584046 0.0020700 0.0395610 2.623607
stl 1995 Jul 2.446975 2.581489 0.0298788 -0.1643929 2.417096
stl 1995 Aug 2.283491 2.589679 -0.0002381 -0.3059498 2.283729
stl 1995 Sep 2.332737 2.597869 -0.0630000 -0.2021313 2.395738
stl 1995 Oct 2.355041 2.606059 -0.0196444 -0.2313733 2.374685
stl 1995 Nov 2.897337 2.616718 0.0427982 0.2378208 2.854539
stl 1995 Dec 2.761315 2.627378 0.0192696 0.1146676 2.742046
stl 1996 Jan 2.679809 2.638038 -0.0306092 0.0723806 2.710418
stl 1996 Feb 2.887291 2.648316 0.0242794 0.2146955 2.863011
stl 1996 Mar 2.836600 2.658593 0.0424650 0.1355417 2.794135
stl 1996 Apr 2.921793 2.668871 0.0011281 0.2517936 2.920665
stl 1996 May 2.432902 2.667143 -0.0639402 -0.1703010 2.496843
stl 1996 Jun 2.445528 2.665416 -0.0252273 -0.1946604 2.470756
stl 1996 Jul 2.720644 2.663689 0.0297838 0.0271714 2.690860
stl 1996 Aug 2.562643 2.655118 0.0042525 -0.0967271 2.558391
stl 1996 Sep 2.534155 2.646548 -0.0472941 -0.0650986 2.581449
stl 1996 Oct 2.669778 2.637977 0.0067504 0.0250506 2.663028
stl 1996 Nov 2.642216 2.638401 0.0554593 -0.0516438 2.586757
stl 1996 Dec 2.682374 2.638825 0.0264600 0.0170895 2.655914
stl 1997 Jan 2.727599 2.639249 -0.0196566 0.1080063 2.747255
stl 1997 Feb 2.746914 2.646333 0.0363158 0.0642651 2.710598
stl 1997 Mar 2.628667 2.653417 0.0286271 -0.0533776 2.600039
stl 1997 Apr 2.524138 2.660501 -0.0220171 -0.1143464 2.546155
stl 1997 May 2.656771 2.659065 -0.0838669 0.0815730 2.740638
stl 1997 Jun 2.593845 2.657628 -0.0522829 -0.0115007 2.646128
stl 1997 Jul 2.507135 2.656192 0.0298815 -0.1789386 2.477253
stl 1997 Aug 2.894904 2.642698 0.0086911 0.2435145 2.886213
stl 1997 Sep 2.713364 2.629204 -0.0318852 0.1160452 2.745249
stl 1997 Oct 2.721785 2.615710 0.0324531 0.0736219 2.689332
stl 1997 Nov 2.721577 2.604167 0.0670330 0.0503770 2.654544
stl 1997 Dec 2.528965 2.592624 0.0320501 -0.0957095 2.496915
stl 1998 Jan 2.581207 2.581081 -0.0449345 0.0450602 2.626141
stl 1998 Feb 2.625677 2.582949 -0.0006190 0.0433467 2.626296
stl 1998 Mar 2.446975 2.584817 0.0230917 -0.1609334 2.423883
stl 1998 Apr 2.283491 2.586685 -0.0131361 -0.2900574 2.296627
stl 1998 May 2.332737 2.596561 -0.0713332 -0.1924903 2.404071
stl 1998 Jun 2.355041 2.606437 -0.0285087 -0.2228875 2.383550
stl 1998 Jul 2.897337 2.616313 0.0493771 0.2316469 2.847960
stl 1998 Aug 2.761315 2.627607 0.0341515 0.0995564 2.727164
stl 1998 Sep 2.679809 2.638901 -0.0265405 0.0674484 2.706350
stl 1998 Oct 2.887291 2.650196 0.0338159 0.2032792 2.853475
stl 1998 Nov 2.836600 2.657871 0.0473136 0.1314159 2.789286
stl 1998 Dec 2.921793 2.665545 0.0044486 0.2517987 2.917344
stl 1999 Jan 2.432902 2.673220 -0.0694798 -0.1708383 2.502382
stl 1999 Feb 2.445528 2.667107 -0.0367023 -0.1848768 2.482231
stl 1999 Mar 2.720644 2.660994 0.0185267 0.0411226 2.702117
stl 1999 Apr 2.562643 2.654881 -0.0035243 -0.0887136 2.566168
stl 1999 May 2.534155 2.647834 -0.0583082 -0.0553707 2.592463
stl 1999 Jun 2.669778 2.640786 -0.0046894 0.0336815 2.674467
stl 1999 Jul 2.642216 2.633738 0.0684715 -0.0599934 2.573745
stl 1999 Aug 2.682374 2.637476 0.0587682 -0.0138696 2.623606
stl 1999 Sep 2.727599 2.641213 -0.0224823 0.1088675 2.750081
stl 1999 Oct 2.746914 2.644951 0.0336918 0.0682712 2.713222
stl 1999 Nov 2.628667 2.650009 0.0259071 -0.0472494 2.602759
stl 1999 Dec 2.524138 2.655067 -0.0246154 -0.1063138 2.548753
stl 2000 Jan 2.656771 2.660125 -0.0761919 0.0728377 2.732963
stl 2000 Feb 2.593845 2.655403 -0.0383692 -0.0231892 2.632214
stl 2000 Mar 2.507135 2.650681 0.0350129 -0.1785595 2.472122
stl 2000 Apr 2.894904 2.645960 0.0191572 0.2297869 2.875746
stl 2000 May 2.713364 2.631239 -0.0402334 0.1223582 2.753598
stl 2000 Jun 2.721785 2.616519 0.0202366 0.0850295 2.701549
stl 2000 Jul 2.721577 2.601799 0.0605776 0.0592005 2.661000
stl 2000 Aug 2.528965 2.594502 0.0244997 -0.0900366 2.504465
stl 2000 Sep 2.581207 2.587204 -0.0446383 0.0386408 2.625845
stl 2000 Oct 2.625677 2.579907 -0.0001033 0.0458731 2.625780
stl 2000 Nov 2.446975 2.585240 0.0240761 -0.1623411 2.422899
stl 2000 Dec 2.283491 2.590574 -0.0118297 -0.2952527 2.295321
stl 2001 Jan 2.332737 2.595907 -0.0795996 -0.1835699 2.412337
stl 2001 Feb 2.355041 2.606106 -0.0374115 -0.2136535 2.392452
stl 2001 Mar 2.897337 2.616305 0.0534441 0.2275884 2.843893
stl 2001 Apr 2.761315 2.626504 0.0431161 0.0916954 2.718199
stl 2001 May 2.679809 2.637636 -0.0215487 0.0637220 2.701358
stl 2001 Jun 2.887291 2.648768 0.0452489 0.1932732 2.842042
stl 2001 Jul 2.836600 2.659901 0.0522464 0.1244530 2.784354
stl 2001 Aug 2.921793 2.663612 -0.0105160 0.2686967 2.932309
stl 2001 Sep 2.432902 2.667323 -0.0678517 -0.1665694 2.500754
stl 2001 Oct 2.445528 2.671035 -0.0351062 -0.1904002 2.480634
stl 2001 Nov 2.720644 2.663394 0.0208868 0.0363628 2.699757
stl 2001 Dec 2.562643 2.655753 -0.0004677 -0.0926422 2.563111
stl 2002 Jan 2.534155 2.648113 -0.0550359 -0.0589220 2.589191
stl 2002 Feb 2.669778 2.643774 -0.0024137 0.0284176 2.672192
stl 2002 Mar 2.642216 2.639436 0.0603469 -0.0575660 2.581870
stl 2002 Apr 2.682374 2.635097 0.0376120 0.0096655 2.644762
stl 2002 May 2.727599 2.641295 -0.0309695 0.1172732 2.758568
stl 2002 Jun 2.746914 2.647493 0.0222677 0.0771536 2.724646
stl 2002 Jul 2.628667 2.653690 0.0348995 -0.0599233 2.593767
stl 2002 Aug 2.524138 2.655454 -0.0122532 -0.1190630 2.536391
stl 2002 Sep 2.656771 2.657218 -0.0758244 0.0753777 2.732595
stl 2002 Oct 2.593845 2.658981 -0.0390803 -0.0260560 2.632925
stl 2002 Nov 2.507135 2.649272 0.0339621 -0.1760990 2.473173
stl 2002 Dec 2.894904 2.639562 0.0179079 0.2374336 2.876996
stl 2003 Jan 2.713364 2.629853 -0.0346213 0.1181327 2.747985
stl 2003 Feb 2.721785 2.616259 0.0290112 0.0765146 2.692774
stl 2003 Mar 2.721577 2.602666 0.0642526 0.0546583 2.657325
stl 2003 Apr 2.528965 2.589073 0.0300126 -0.0901209 2.498952
stl 2003 May 2.581207 2.586594 -0.0415837 0.0361966 2.622790
stl 2003 Jun 2.625677 2.584114 -0.0008186 0.0423809 2.626495
stl 2003 Jul 2.446975 2.581635 0.0185360 -0.1531959 2.428439
stl 2003 Aug 2.283491 2.589999 -0.0119577 -0.2945501 2.295449
stl 2003 Sep 2.332737 2.598363 -0.0807152 -0.1849102 2.413453
stl 2003 Oct 2.355041 2.606727 -0.0392002 -0.2124856 2.394241
stl 2003 Nov 2.897337 2.617211 0.0516640 0.2284619 2.845673
stl 2003 Dec 2.761315 2.627696 0.0412326 0.0923867 2.720083
stl 2004 Jan 2.679809 2.638181 -0.0268069 0.0684356 2.706616
stl 2004 Feb 2.887291 2.648138 0.0329517 0.2062009 2.854339
stl 2004 Mar 2.836600 2.658095 0.0466843 0.1318206 2.789916
stl 2004 Apr 2.921793 2.668052 0.0041746 0.2495658 2.917618
stl 2004 May 2.432902 2.666495 -0.0626330 -0.1709601 2.495535
stl 2004 Jun 2.445528 2.664938 -0.0264736 -0.1929365 2.472002
stl 2004 Jul 2.720644 2.663381 0.0242707 0.0329915 2.696373
stl 2004 Aug 2.562643 2.655177 -0.0014845 -0.0910489 2.564128
stl 2004 Sep 2.534155 2.646972 -0.0560645 -0.0567529 2.590219
stl 2004 Oct 2.669778 2.638768 -0.0029518 0.0339623 2.672730
stl 2004 Nov 2.642216 2.639096 0.0599975 -0.0568774 2.582219
stl 2004 Dec 2.682374 2.639425 0.0375649 0.0053843 2.644810
stl 2005 Jan 2.727599 2.639754 -0.0192933 0.1071380 2.746892
stl 2005 Feb 2.746914 2.646514 0.0366543 0.0637450 2.710260
stl 2005 Mar 2.628667 2.653275 0.0289408 -0.0535494 2.599726
stl 2005 Apr 2.524138 2.660036 -0.0217541 -0.1141440 2.545892
stl 2005 May 2.656771 2.658641 -0.0836885 0.0818187 2.740459
stl 2005 Jun 2.593845 2.657246 -0.0521855 -0.0112154 2.646030
stl 2005 Jul 2.507135 2.655851 0.0298978 -0.1786136 2.477237
stl 2005 Aug 2.894904 2.642478 0.0086166 0.2438088 2.886287
stl 2005 Sep 2.713364 2.629106 -0.0320504 0.1163087 2.745415
stl 2005 Oct 2.721785 2.615734 0.0322335 0.0738182 2.689552
stl 2005 Nov 2.721577 2.604196 0.0668413 0.0505403 2.654736
stl 2005 Dec 2.528965 2.592658 0.0319033 -0.0955962 2.497062
stl 2006 Jan 2.581207 2.581120 -0.0450043 0.0450912 2.626211
stl 2006 Feb 2.625677 2.582981 -0.0006284 0.0433237 2.626305
stl 2006 Mar 2.446975 2.584843 0.0231428 -0.1610103 2.423832
stl 2006 Apr 2.283491 2.586704 -0.0130371 -0.2901758 2.296528
stl 2006 May 2.332737 2.596575 -0.0712436 -0.1925943 2.403981
stl 2006 Jun 2.355041 2.606447 -0.0284325 -0.2229733 2.383473
stl 2006 Jul 2.897337 2.616318 0.0494399 0.2315794 2.847898
stl 2006 Aug 2.761315 2.627612 0.0341588 0.0995443 2.727156
stl 2006 Sep 2.679809 2.638906 -0.0265887 0.0674916 2.706398
stl 2006 Oct 2.887291 2.650201 0.0337121 0.2033779 2.853578
stl 2006 Nov 2.836600 2.657875 0.0472244 0.1315006 2.789376
stl 2006 Dec 2.921793 2.665550 0.0043737 0.2518696 2.917419
stl 2007 Jan 2.432902 2.673224 -0.0695749 -0.1707468 2.502477
stl 2007 Feb 2.445528 2.667109 -0.0367294 -0.1848515 2.482258
stl 2007 Mar 2.720644 2.660994 0.0185675 0.0410818 2.702076
stl 2007 Apr 2.562643 2.654880 -0.0034155 -0.0888207 2.566059
stl 2007 May 2.534155 2.647831 -0.0582122 -0.0554638 2.592367
stl 2007 Jun 2.669778 2.640782 -0.0046060 0.0336022 2.674384
stl 2007 Jul 2.642216 2.633733 0.0685424 -0.0600590 2.573674
stl 2007 Aug 2.682374 2.637472 0.0587878 -0.0138852 2.623587
stl 2007 Sep 2.727599 2.641210 -0.0225138 0.1089020 2.750112
stl 2007 Oct 2.746914 2.644949 0.0336092 0.0683556 2.713305
stl 2007 Nov 2.628667 2.650009 0.0258315 -0.0471743 2.602835
stl 2007 Dec 2.524138 2.655070 -0.0246841 -0.1062479 2.548822
stl 2008 Jan 2.656771 2.660130 -0.0762459 0.0728866 2.733017
stl 2008 Feb 2.593845 2.655407 -0.0383856 -0.0231772 2.632230
stl 2008 Mar 2.507135 2.650685 0.0350342 -0.1785843 2.472101
stl 2008 Apr 2.894904 2.645962 0.0192160 0.2297254 2.875688
stl 2008 May 2.713364 2.631240 -0.0401806 0.1223051 2.753545
stl 2008 Jun 2.721785 2.616517 0.0202834 0.0849848 2.701502
stl 2008 Jul 2.721577 2.601795 0.0606183 0.0591643 2.660959
stl 2008 Aug 2.528965 2.594498 0.0245139 -0.0900468 2.504451
stl 2008 Sep 2.581207 2.587201 -0.0446507 0.0386565 2.625857
stl 2008 Oct 2.625677 2.579904 -0.0001422 0.0459148 2.625819
stl 2008 Nov 2.446975 2.585240 0.0240406 -0.1623053 2.422935
stl 2008 Dec 2.283491 2.590576 -0.0118618 -0.2952227 2.295353
stl 2009 Jan 2.332737 2.595911 -0.0796112 -0.1835627 2.412349
stl 2009 Feb 2.355041 2.606110 -0.0374165 -0.2136528 2.392457
stl 2009 Mar 2.897337 2.616309 0.0534459 0.2275826 2.843891
stl 2009 Apr 2.761315 2.626508 0.0431245 0.0916832 2.718191
stl 2009 May 2.679809 2.637638 -0.0215403 0.0637115 2.701350
stl 2009 Jun 2.887291 2.648769 0.0452572 0.1932646 2.842033
stl 2009 Jul 2.836600 2.659899 0.0522545 0.1244463 2.784346
stl 2009 Aug 2.921793 2.663610 -0.0105103 0.2686927 2.932303
stl 2009 Sep 2.432902 2.667321 -0.0678484 -0.1665708 2.500751
stl 2009 Oct 2.445528 2.671033 -0.0351052 -0.1903991 2.480634
stl 2009 Nov 2.720644 2.663392 0.0208873 0.0363640 2.699756
stl 2009 Dec 2.562643 2.655752 -0.0004676 -0.0926412 2.563111
stl 2010 Jan 2.534155 2.648112 -0.0550437 -0.0589135 2.589199
stl 2010 Feb 2.669778 2.643774 -0.0024182 0.0284226 2.672196
stl 2010 Mar 2.642216 2.639435 0.0603455 -0.0575644 2.581871
stl 2010 Apr 2.682374 2.635097 0.0376139 0.0096634 2.644760
stl 2010 May 2.727599 2.641295 -0.0309674 0.1172711 2.758566
stl 2010 Jun 2.746914 2.647493 0.0222698 0.0771514 2.724644
stl 2010 Jul 2.628667 2.653690 0.0349018 -0.0599255 2.593765
stl 2010 Aug 2.524138 2.655454 -0.0122518 -0.1190642 2.536390
stl 2010 Sep 2.656771 2.657217 -0.0758239 0.0753776 2.732595
stl 2010 Oct 2.593845 2.658981 -0.0390808 -0.0260552 2.632926
stl 2010 Nov 2.507135 2.649271 0.0339616 -0.1760982 2.473173
stl 2010 Dec 2.894904 2.639562 0.0179073 0.2374342 2.876996
stl 2011 Jan 2.713364 2.629853 -0.0346215 0.1181328 2.747986
stl 2011 Feb 2.721785 2.616260 0.0290110 0.0765145 2.692774
stl 2011 Mar 2.721577 2.602667 0.0642524 0.0546582 2.657325
stl 2011 Apr 2.528965 2.589074 0.0300122 -0.0901211 2.498953
stl 2011 May 2.581207 2.586594 -0.0415841 0.0361965 2.622791
stl 2011 Jun 2.625677 2.584115 -0.0008193 0.0423808 2.626496
stl 2011 Jul 2.446975 2.581636 0.0185352 -0.1531958 2.428440
stl 2011 Aug 2.283491 2.589999 -0.0119587 -0.2945496 2.295450
stl 2011 Sep 2.332737 2.598363 -0.0807164 -0.1849093 2.413454
stl 2011 Oct 2.355041 2.606727 -0.0392017 -0.2124843 2.394243
stl 2011 Nov 2.897337 2.617211 0.0516623 0.2284637 2.845675
stl 2011 Dec 2.761315 2.627696 0.0412306 0.0923890 2.720085
stl 2012 Jan 2.679809 2.638180 -0.0268062 0.0684354 2.706615
stl 2012 Feb 2.887291 2.648137 0.0329534 0.2061997 2.854337
stl 2012 Mar 2.836600 2.658095 0.0466869 0.1318184 2.789913
stl 2012 Apr 2.921793 2.668052 0.0041782 0.2495626 2.917615
stl 2012 May 2.432902 2.666495 -0.0626296 -0.1709634 2.495532
stl 2012 Jun 2.445528 2.664939 -0.0264704 -0.1929399 2.471999
stl 2012 Jul 2.720644 2.663382 0.0242738 0.0329880 2.696370
stl 2012 Aug 2.562643 2.655177 -0.0014853 -0.0910484 2.564129
stl 2012 Sep 2.534155 2.646972 -0.0560691 -0.0567485 2.590224
stl 2012 Oct 2.669778 2.638768 -0.0029602 0.0339707 2.672738
stl 2012 Nov 2.642216 2.639096 0.0599900 -0.0568697 2.582226
stl 2012 Dec 2.682374 2.639425 0.0375585 0.0053913 2.644816
stl 2013 Jan 2.727599 2.639753 -0.0192918 0.1071372 2.746890
stl 2013 Feb 2.746914 2.646514 0.0366581 0.0637419 2.710256
stl 2013 Mar 2.628667 2.653275 0.0289470 -0.0535550 2.599720
stl 2013 Apr 2.524138 2.660036 -0.0217458 -0.1141519 2.545884
stl 2013 May 2.656771 2.658642 -0.0836804 0.0818095 2.740451
stl 2013 Jun 2.593845 2.657248 -0.0521779 -0.0112255 2.646023
stl 2013 Jul 2.507135 2.655854 0.0299050 -0.1786246 2.477230
stl 2013 Aug 2.894904 2.642482 0.0086156 0.2438060 2.886288
stl 2013 Sep 2.713364 2.629110 -0.0320596 0.1163141 2.745424
stl 2013 Oct 2.721785 2.615737 0.0322163 0.0738317 2.689569
stl 2013 Nov 2.721577 2.604196 0.0668256 0.0505558 2.654752
stl 2013 Dec 2.528965 2.592654 0.0318894 -0.0955790 2.497075
stl 2014 Jan 2.581207 2.581113 -0.0450640 0.0451577 2.626271
stl 2014 Feb 2.625677 2.582974 -0.0006511 0.0433538 2.626328
stl 2014 Mar 2.446975 2.584835 0.0231570 -0.1610167 2.423818
stl 2014 Apr 2.283491 2.586696 -0.0129858 -0.2902188 2.296477
stl 2014 May 2.332737 2.596571 -0.0711809 -0.1926531 2.403918
stl 2014 Jun 2.355041 2.606447 -0.0283583 -0.2230480 2.383399
stl 2014 Jul 2.897337 2.616323 0.0495256 0.2314889 2.847812
stl 2014 Aug 2.761315 2.627618 0.0341894 0.0995081 2.727126
stl 2014 Sep 2.679809 2.638913 -0.0266133 0.0675098 2.706423
stl 2014 Oct 2.887291 2.650208 0.0336324 0.2034503 2.853658
stl 2014 Nov 2.836600 2.657878 0.0471263 0.1315960 2.789474
stl 2014 Dec 2.921793 2.665548 0.0042574 0.2519879 2.917535
stl 2015 Jan 2.432902 2.673217 -0.0696875 -0.1706275 2.502590
stl 2015 Feb 2.445528 2.667100 -0.0367696 -0.1848022 2.482298
stl 2015 Mar 2.720644 2.660983 0.0185998 0.0410610 2.702044
stl 2015 Apr 2.562643 2.654866 -0.0033100 -0.0889122 2.565953
stl 2015 May 2.534155 2.647820 -0.0580825 -0.0555826 2.592237
stl 2015 Jun 2.669778 2.640774 -0.0044512 0.0334552 2.674229
stl 2015 Jul 2.642216 2.633728 0.0687223 -0.0602342 2.573494
stl 2015 Aug 2.682374 2.637471 0.0588675 -0.0139639 2.623507
stl 2015 Sep 2.727599 2.641213 -0.0225345 0.1089196 2.750133
stl 2015 Oct 2.746914 2.644956 0.0334881 0.0684697 2.713426
stl 2015 Nov 2.628667 2.650017 0.0256739 -0.0470247 2.602993
stl 2015 Dec 2.524138 2.655079 -0.0248787 -0.1060623 2.549017
stl 2016 Jan 2.656771 2.660140 -0.0763963 0.0730270 2.733167
stl 2016 Feb 2.593845 2.655414 -0.0384580 -0.0231113 2.632303
stl 2016 Mar 2.507135 2.650688 0.0350398 -0.1785928 2.472095
stl 2016 Apr 2.894904 2.645962 0.0192993 0.2296428 2.875604
stl 2016 May 2.713364 2.631231 -0.0400675 0.1222005 2.753432
stl 2016 Jun 2.721785 2.616501 0.0204262 0.0848583 2.701359
stl 2016 Jul 2.721577 2.601770 0.0607909 0.0590159 2.660786
stl 2016 Aug 2.528965 2.594451 0.0246087 -0.0900950 2.504356
stl 2016 Sep 2.581207 2.587132 -0.0446337 0.0387086 2.625840
stl 2016 Oct 2.625677 2.579813 -0.0001968 0.0460608 2.625873
stl 2016 Nov 2.446975 2.585081 0.0239688 -0.1620752 2.423006
stl 2016 Dec 2.283491 2.590351 -0.0119208 -0.2949386 2.295412
stl 2017 Jan 2.332737 2.595619 -0.0797231 -0.1831589 2.412460
stl 2017 Feb 2.355041 2.605688 -0.0373424 -0.2133044 2.392383
stl 2017 Mar 2.897337 2.615756 0.0537060 0.2278755 2.843631
stl 2017 Apr 2.761315 2.625824 0.0436560 0.0918352 2.717659
stl 2017 May 2.679809 2.636919 -0.0207838 0.0636740 2.700593
stl 2017 Jun 2.887291 2.648014 0.0462994 0.1929768 2.840991
stl 2017 Jul 2.836600 2.659110 0.0535824 0.1239081 2.783018
stl 2017 Aug 2.921793 2.663231 -0.0089730 0.2675345 2.930766
stl 2017 Sep 2.432902 2.667353 -0.0661018 -0.1683489 2.499004
stl 2017 Oct 2.445528 2.671475 -0.0331633 -0.1927831 2.478692
stl 2017 Nov 2.720644 2.663989 0.0230691 0.0335857 2.697575
stl 2017 Dec 2.562643 2.656503 0.0019439 -0.0958036 2.560700
stl 2018 Jan 2.534155 2.649017 -0.0553964 -0.0594662 2.589551
stl 2018 Feb 2.669778 2.644191 -0.0080411 0.0336281 2.677819
stl 2018 Mar 2.642216 2.639365 0.0508204 -0.0479689 2.591396
stl 2018 Apr 2.682374 2.634539 0.0276601 0.0201756 2.654714
stl 2018 May 2.727599 2.640607 -0.0358639 0.1228556 2.763463
stl 2018 Jun 2.746914 2.646675 0.0179688 0.0822701 2.728945
stl 2018 Jul 2.628667 2.652743 0.0475739 -0.0716504 2.581093
stl 2018 Aug 2.524138 2.655041 -0.0006442 -0.1302596 2.524782
stl 2018 Sep 2.656771 2.657340 -0.0645569 0.0639879 2.721328
stl 2018 Oct 2.593845 2.659638 -0.0229880 -0.0428056 2.616833
stl 2018 Nov 2.507135 2.650271 0.0336190 -0.1767548 2.473516
stl 2018 Dec 2.894904 2.640903 0.0121991 0.2418019 2.882705
stl 2019 Jan 2.713364 2.631535 -0.0348194 0.1166487 2.748184
stl 2019 Feb 2.721785 2.617743 0.0177402 0.0863023 2.704045
stl 2019 Mar 2.721577 2.603951 0.0446448 0.0729818 2.676932
stl 2019 Apr 2.528965 2.590158 0.0087790 -0.0699727 2.520186
stl 2019 May 2.581207 2.587585 -0.0534241 0.0470453 2.634631
stl 2019 Jun 2.625677 2.585012 -0.0123481 0.0530122 2.638025
stl 2019 Jul 2.446975 2.582439 0.0400730 -0.1755374 2.406902
stl 2019 Aug 2.283491 2.590265 0.0066553 -0.3134288 2.276836
stl 2019 Sep 2.332737 2.598090 -0.0635784 -0.2017739 2.396316
stl 2019 Oct 2.355041 2.605915 -0.0130870 -0.2377871 2.368128
stl 2019 Nov 2.897337 2.615950 0.0441867 0.2372011 2.853151
stl 2019 Dec 2.761315 2.625984 0.0225288 0.1128024 2.738786
stl 2020 Jan 2.679809 2.636019 -0.0290407 0.0728313 2.708850
stl 2020 Feb 2.887291 2.646878 0.0253623 0.2150505 2.861928
stl 2020 Mar 2.836600 2.657737 0.0419430 0.1369204 2.794657
stl 2020 Apr 2.921793 2.668596 0.0006939 0.2525032 2.921099
stl 2020 May 2.432902 2.667521 -0.0598891 -0.1747293 2.492791
stl 2020 Jun 2.445528 2.666446 -0.0224232 -0.1984943 2.467951
stl 2020 Jul 2.720644 2.665371 0.0382860 0.0169869 2.682358
stl 2020 Aug 2.562643 2.656478 0.0061100 -0.0999447 2.556534
stl 2020 Sep 2.534155 2.647586 -0.0646226 -0.0488082 2.598777
stl 2020 Oct 2.669778 2.638693 -0.0111697 0.0422549 2.680948
stl 2020 Nov 2.642216 2.638400 0.0481232 -0.0443071 2.594093
stl 2020 Dec 2.682374 2.638108 0.0289661 0.0153005 2.653408
stl 2021 Jan 2.727599 2.637815 -0.0227607 0.1125440 2.750359
stl 2021 Feb 2.746914 2.645351 0.0335304 0.0680321 2.713383
stl 2021 Mar 2.628667 2.652887 0.0398320 -0.0640526 2.588835
stl 2021 Apr 2.524138 2.660423 -0.0068059 -0.1294796 2.530944
stl 2021 May 2.656771 2.658825 -0.0657746 0.0637206 2.722545
stl 2021 Jun 2.593845 2.657226 -0.0319894 -0.0313923 2.625834
stl 2021 Jul 2.507135 2.655628 0.0369371 -0.1854303 2.470198
stl 2021 Aug 2.894904 2.641636 0.0058789 0.2473893 2.889025
stl 2021 Sep 2.713364 2.627643 -0.0654763 0.1511975 2.778840
stl 2021 Oct 2.721785 2.613650 -0.0091856 0.1173205 2.730971
stl 2021 Nov 2.721577 2.603086 0.0520030 0.0664879 2.669574
stl 2021 Dec 2.528965 2.592522 0.0352651 -0.0988226 2.493700
stl 2022 Jan 2.581207 2.581958 -0.0179098 0.0171583 2.599117
stl 2022 Feb 2.625677 2.593561 0.0399127 -0.0077973 2.585764
stl 2022 Mar 2.446975 2.605164 0.0386426 -0.1968315 2.408333
stl 2022 Apr 2.283491 2.616767 -0.0114146 -0.3218612 2.294906
stl 2022 May 2.332737 2.635235 -0.0701715 -0.2323258 2.402909
stl 2022 Jun 2.355041 2.653703 -0.0392171 -0.2594445 2.394258
stl 2022 Jul 2.897337 2.672170 0.0348023 0.1903647 2.862535
stl 2022 Aug 2.761315 2.695079 0.0057613 0.0604752 2.755554
stl 2022 Sep 2.679809 2.717987 -0.0656563 0.0274783 2.745466
stl 2022 Oct 2.887291 2.740896 -0.0073159 0.1537106 2.894606
stl 2022 Nov 2.836600 2.768509 0.0550684 0.0130221 2.781532
stl 2022 Dec 2.921793 2.796123 0.0390920 0.0865776 2.882701
components(dcmptsm) |>
  as_tsibble() |>
  autoplot(value, colour="red") +
  geom_line(aes(y=trend), colour = "black") +
  labs(
    y = "TSM",
    title = "Serie de tiempo descompuesta de TSM Cover en 48.1"
  ) +
  theme_bw()

Ahora lo descompongo en los demas componentes

components(dcmptsm) |> 
  autoplot(colour="red") +
  theme_bw()

Model ARIMA

traintsm <- dtats2$meantsm2[1:32]
testtsm <- dtats$meansic[33:40]

modeltsm <- arima(traintsm, order =c(1,2,1))

predotsm <- forecast::forecast(modeltsm, h=10)
plot(predotsm)

Moving Average.

mov_avgtsm <- zoo::rollmean(dtats2$meantsm2, k=3, fill=NA)


predictiontsm <- tail(mov_avgtsm, n=5)

ggplot() + 
  geom_line(aes(x = dtats2$ANOn, y = dtats2$meantsm2), 
            data = dtats, color = "blue") +
  geom_line(aes(x = dtats2$ANOn, y = mov_avgtsm), 
            data =dtats, color = "red") +
  geom_hline(yintercept = predictiontsm[1], color = "green") +
  xlab("Fecha") +
  ylab("Datos") +
  ggtitle("Datos y media móvil") +
  theme_bw()